Problem: Simplify; express your answer in exponential form. Assume $n\neq 0, p\neq 0$. $\dfrac{{n^{-2}p^{-1}}}{{(n^{-1}p^{5})^{2}}}$
Answer: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${n^{-2}p^{-1} = n^{-2}p^{-1}}$ On the left, we have ${n^{-2}}$ to the exponent ${1}$ . Now ${-2 \times 1 = -2}$ , so ${n^{-2} = n^{-2}}$ Apply the ideas above to simplify the equation. $\dfrac{{n^{-2}p^{-1}}}{{(n^{-1}p^{5})^{2}}} = \dfrac{{n^{-2}p^{-1}}}{{n^{-2}p^{10}}}$ Break up the equation by variable and simplify. $\dfrac{{n^{-2}p^{-1}}}{{n^{-2}p^{10}}} = \dfrac{{n^{-2}}}{{n^{-2}}} \cdot \dfrac{{p^{-1}}}{{p^{10}}} = n^{{-2} - {(-2)}} \cdot p^{{-1} - {10}} = p^{-11}$